4 articles.
One bimodal target, one Gaussian, and two directions of the same divergence. Minimising KL(P||Q) puts the Gaussian across both modes with almost no mass where the target actually lives; minimising KL(Q||P) puts it on one mode at a value of 0.6931 nats, which is ln 2 to four decimals and not a coincidence. Each fit is judged catastrophic by the other objective, 2.0976 against 15.2799.
A variable that determines another with a correlation of exactly 0.0000000000, and a pair of features whose every pairwise mutual information with the target is exactly zero while the two together determine it completely. Univariate screening discards both, and the second case is the one that matters: the features it removes are removed because they matter.
Entropy is not a summary of a distribution but a floor that the best code meets to the last decimal, the surcharge for using the wrong distribution is exactly the loss every classifier already minimises, and mutual information puts a hard ceiling on everything downstream of a sensor. Three results, each unusually sharp.
Measuring uncertainty in bits: Shannon entropy and why the logarithm is base 2, information gain worked on a split, and how cross-entropy and KL divergence relate to entropy and to the loss functions used to train classifiers.